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| Laywine C.F., Mullen G.L. — Discrete Mathematics Using Latin Squares |
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| Предметный указатель |
(t, m, s)-Nets 241—254
(t, m, s)-Nets and coding theory 250
(t, m, s)-Nets and error-correcting codes 250 254
(t, m, s)-Nets and MOLS 244—250 253 254
Affine geometries 161—166 171 173
Affine geometries, k-flats defined 161
Affine plant(s) 68—70
Affine plant(s), algebraic derivation 133—136
Affine plant(s), axioms, defining 131
Affine plant(s), defargueuaa 143—146
Affine plant(s), nondesarguesian 146—150
Affine plant(s), order or finite 132
Agrippa, C 17
Algebraic background 269—277
anova 188 201
Axial classes 289
Background, algebraic 269—277
Balanced incomplete block design 153
Bipartite graph 287
Bose 1938
Bose, equivalence 137
Brack (geometric) nets 247
Brack- Ryser theorem 152
Brouwer, table from 213 215 219 220 226
Bye-boards 182
Casanova, and magic squares 176
Cayley (multiplication) table 95 103
Cayley theorem 96
Characterizing graphs with Hamilton cycles, problem 106
Classes, axial 289
Codecs and latin squares 205—226
Codecs from MOFS 215 226
Codecs from MOLS 209—213
Codecs from orthogonal hypercubes 216
Codecs, binary 205
Codecs, constant weight 217 218
Codecs, error-correcting 123 205—226
Codecs, Golomb — Posner MDS 213 216 226
Codecs, linear 206
Codecs, maximum distance separable (MDS), defined 212 213
Codecs, nonlinear 208
Codecs, optimal 213—221
Codecs, projective 219 4
Codecs, q-ary 205
Codecs, rate of 208
Codecs, repetition, of length ft 209 210
Codecs, ternary 205
Codecs, two weight 219
Codecs, weight (wt) 207
Column effects 190
Commutative ring 270
Critical set(s) 231 238 239 293
Critical set(s), and  latin square 293
Critical set(s), minimal 231 238 239
Cryptology and latin squares 228—239
Cryptology and latin squares, ciphertexts 228
Cryptology and latin squares, cryptology, cryptography, and cryptoanalysis defined 228
Cryptology and latin squares, enciphering and deciphering 228
Cryptology and latin squares, multilevel 232
Cryptology and latin squares, secret sharing schemes 230—233
Cryptology and latin squares, shadows of secret key 230
Cryptology and latin squares, shares of secret key 230
Deficiency of a set of MOLS 33 122
Derangement 78
Desargues configuration 143—146
Desargues configuration, affine formulation 146
Desargues configuration, defined 143
Desargues theorem 144 145
Desarguesian plane(s) 172
Desarguesian set of MOLS 22 35
Desarguesian set of MOLS, construction ot 21 22
Designs, affine resolvable 155 171—173
Designs, balanced incomplete block 153—155
Designs, resolvable 155
Designs, symmetric 155
Designs, transversal 27—32 37
Digital signature 237
Discordant permutation 77
Discrete logarithm cryptosystems 234—239
Discrete logarithm cryptosystems and Euler's function p 237 271
Discrete logarithm cryptosystems, no-key 236 237
Discrete logarithm cryptosystems, public-key 237 238
Discrete logarithm cryptosystems, RSA (Rivest, Shamir, and Adleman) 237—240
Discrete logarithm cryptosystems, three pass system 236 237
Discrete logarithm problem 103 234 239
Division algorithm 269
Duerer, Melencolia I engraving 17
Elementary intervals 242 243
Error-correcting codes (see Code(s) error-correcting)
Euclidean plane(s) 131 133 136 143
Euler 36-officer problem 5—8 11 23 58 64 67 101 104 122 127 188
Euler bound 58—60
Euler circuit 119 120
Euler conjecture 8 23 26 27 37 8 101 104
Euler solution of Kdnigsberg bridge problem 106 127
Fermat last theorem 106
Fermat primes 291
Fields and irreducible polynomials 272 273 277 278 280
fields, defined 270
Fields, finite 271 278
Fields, Galois 273
Fields, properties of 274
Finite field 20 21 270—274 278
Finite field, primitive elements 274 277 291
Four color problem 106 126
Fractional replication plains) 226
Frequency square(s) 63—70
Frequency square(s) constant frequency 64
Frequency square(s) defined 63
Frequency square(s) nonconstant frequency 70
Frequency square(s) orthogonal sets of 63 64
Galois field 273
Generalized orthogonal array 251
Generator matrices 214—217 292
Geometric (Brack) nets 247
Geometric hypercubes, defined 163
Golf design 13
Graphs (and latin squares) 106—128
Graphs (and latin squares), 1-factor(ization) 107 126 286 287
Graphs (and latin squares), adjacency matrix 112
Graphs (and latin squares), bipartite 107 126
Graphs (and latin squares), edges 106
Graphs (and latin squares), monochromatic 1-factor 107
Graphs (and latin squares), net 122 126
Graphs (and latin squares), pseudo-net 122
Graphs (and latin squares), regular 121
Graphs (and latin squares), strongly regular 121—123
Graphs (and latin squares), vertices 106
Groups (and latin squares) 94—104
Groups (and latin squares), abelian 94
Groups (and latin squares), associative 94
Groups (and latin squares), commutative 94
Groups (and latin squares), cyclic 94
Groups (and latin squares), defined 94
Groups (and latin squares), examples of 94
Groups (and latin squares), finite 94
Groups (and latin squares), generator 94
Groups (and latin squares), identity element 94
Groups (and latin squares), inverse element 94
Groups (and latin squares), order n 94
Groups (and latin squares), properties of 94
Hall marriage theorem 108 109 287
Hall plane(s) 146 147 151 172
Hamilton circuit(s) 118 119 126 287
Hamilton cycles, characterizing graphs with 106
Hamiltonian path 115 116 126 287
Hamming (sphere-packing) bound 211 224
Hamming distance 206 226 257
Hohler definition of orthogonality 61
Howell master sheets 182 (see also Room squares)
| Hughes polynomials 151 152
Hypercube(s) algorithm for construction from latin squares 294
Hypercube(s) d-dimensional 43
Hypercube(s) from latin squares 294
Hypercube(s) geometric, defined 163
Hypercube(s) latin 43 44
Hypercube(s) nonlatin 44
Hyperplanes 171—173
Hyperrectangles 70
Integers ring of, modulo n 270
Integers, congruent modulo n 269
Intervals, elementary 242 243
Irreducible polynomials 272 273 277 278 280
Kdnigsberg bridge problem 106 127
Knut-Vik designs (pandiagonal latin squares) 179
Kronecker product and hypercubes 57 58
Kronecker product and MOLS 23—27 124 125 280—282
Lagrange interpolation formula 20 274 296
Lagrange interpolation formula and polynomial representation 274
Lagrange theorem 38
Latin rectangle 15 93
Latin rectangle, first row 75 90 91
Latin rectangle, second row 75 84 85
Latin rectangle, third row 85—90
Latin square(s) and geometry 13 14
Latin square(s) and graphs 106—128
Latin square(s) and groups 94—104
Latin square(s) and linear algebra 14
Latin square(s) and statistics. 188—204
Latin square(s) applications 255—265
Latin square(s) applications, agricultural experiments 9—11
Latin square(s) applications, authentication schemes 263 264
Latin square(s) applications, check character systems 263 264
Latin square(s) applications, classic squares and broadcast squares 259 260 264
Latin square(s) applications, code design 11 12 101 102 228—239 263—265
Latin square(s) applications, committee formation 8 9
Latin square(s) applications, compiler testing. 263 265
Latin square(s) applications, cryptography 101 102 205—226 228—239 263—265
Latin square(s) applications, drug test design 11
Latin square(s) applications, experimental design 9—11 264
Latin square(s) applications, golf design 13 262
Latin square(s) applications, hash functions 263 264
Latin square(s) applications, network testing systems 263—265
Latin square(s) applications, tomography 263 265
Latin square(s) applications, tournament design 12 13 260—262
Latin square(s) column complete 115
Latin square(s) complete 115
Latin square(s) defined 3
Latin square(s) diagonal 36
Latin square(s) disjoint transversals 33 36
Latin square(s) generalized 257 264
Latin square(s) idempotent 33 34 36 123 124 282
Latin square(s) introduction to 3—17
Latin square(s) nearly consecutive symbols 263
Latin square(s) order n 279
Latin square(s) orthogonal 5—9 280 281
Latin square(s) orthogonal mates 32 33 36
Latin square(s) orthogonal sets 18 36 37
Latin square(s) orthogonal, pair of 21
Latin square(s) partial 14 15
Latin square(s) perfect 258 264
Latin square(s) perfect and conflict-free access to parallel memories 264
Latin square(s) perfect, main subsquare. 258
Latin square(s), r-orthogonal 257 264
Latin square(s), reduced 4 15 112 113 126
Latin square(s), row 97—100 285
Latin square(s), row complete, II 115 126
Latin square(s), self-orthogonal 33 38 39 282
Latin square(s), symmetric idempotent 13
Latin square(s), transversals of. 36 37
Latin square(s), unipotent 112 113
Loops 97
MacNeish's conjecture 26 27 37
Magic cube 291
Magic squares 175—181 290
Magic squares, 3-dimensional 180
Magic squares, 3-dimensional perfect 180
Magic squares, addition-multiplication 179 180
Magic squares, applications of 175
Magic squares, defined 175
Magic squares, multiplicative properties 181
Magic squares, order 7 181
Manage numbers 86 90 91 93
Melencotia I 175 176
Menage problem 86—89 93
Menage problem, enumeration of 3-row latin rectangles 93
Mersenne primes 291
Moebius inversion 93
MOFS (see Mutually orthogonal frequency squares)
MOHC (see Mutually orthogonal hypercubes)
MOLS (see Mutually orthogonal latin squares)
Monte Carlo methods 253
MOPLS (see Mutually orthogonal partial latin squares)
Moschopoulos, E 175
Multiplication (Cayley) table 95 103
Mutually orthogonal frequency squares (MOFS) 64—70 284 288
Mutually orthogonal frequency squares (MOFS), complete set 64
Mutually orthogonal frequency squares (MOFS), construction by substitution 66—70
Mutually orthogonal frequency squares (MOFS), nonconstant frequency 70
Mutually orthogonal frequency squares (MOFS), polynomial construction 64—66
Mutually orthogonal hypercubes (MOHC) 43—62 247—254 288 289 294
Mutually orthogonal hypercubes (MOHC) and affine designs 153—173
Mutually orthogonal hypercubes (MOHC), blocks 153 171 172
Mutually orthogonal hypercubes (MOHC), complete set 51
Mutually orthogonal hypercubes (MOHC), composition 153
Mutually orthogonal hypercubes (MOHC), defined 44
Mutually orthogonal hypercubes (MOHC), higher orthogonality 250—252
Mutually orthogonal hypercubes (MOHC), Hohler orthogonality 61
Mutually orthogonal hypercubes (MOHC), MacNeish construction 57 58
Mutually orthogonal hypercubes (MOHC), order 6 58 59
Mutually orthogonal hypercubes (MOHC), polynomial construction 47—51 248
Mutually orthogonal hypercubes (MOHC), recursive construction 51—57 61 249 250
Mutually orthogonal hypercubes (MOHC), type 44
Mutually orthogonal Latin squares (MOLS) 18—39 280—282 285 292 294
Mutually orthogonal latin squares (MOLS), and Kronecker product 280 281
Mutually orthogonal latin squares (MOLS), applications 18 37
Mutually orthogonal latin squares (MOLS), complete set 20
Mutually orthogonal latin squares (MOLS), deficiency of a set 33
Mutually orthogonal latin squares (MOLS), defined 19
Mutually orthogonal latin squares (MOLS), Desarguesian construction 21 22
Mutually orthogonal latin squares (MOLS), Desarguesian set 22 35
Mutually orthogonal latin squares (MOLS), isomorphic sets 22 34
Mutually orthogonal latin squares (MOLS), maximum number 19
Mutually orthogonal latin squares (MOLS), nondesarguesian 146 147
Mutually orthogonal latin squares (MOLS), nonisomorphic sets 22
Mutually orthogonal latin squares (MOLS), nonprime power sets 23 24
Mutually orthogonal latin squares (MOLS), polynomial representation 20 21
Mutually orthogonal latin squares (MOLS), power set of 35 36
Mutually orthogonal latin squares (MOLS), prime power sets of 20 21
Mutually orthogonal latin squares (MOLS), sets of nonisomorphic 280
Mutually orthogonal partial latin squares (MOPLS) 255—257 264
Mutually orthogonal partial latin squares (MOPLS), application to computer databases 256 257
Mutually orthogonal partial latin squares (MOPLS), Nets 293—295
Mutually orthogonal partial latin squares (MOPLS), p-compatible 255
Numerical integration 241 242 253
One-way analysis of variance (ANOVAX 188 201
Order, definitions of 102
orthogonal arrays 31 32 36 37 197 246 247 280 281 294
Orthogonal arrays, equivalent objects 31 32
Orthogonal arrays, generalized 251
Orthogonal hypercubes (see Mutually orthogonal hypercubes)
Orthogonal latin square graph (OLSG) 123—126
Orthogonality, Hohler’s definition of 61
Pairwise orthogonal squares 19
Pandiagonal latin squares (Knut-Vik designs) 179
Partial latin square(s) 230 238 239
Permutation cube(s) 43 223 224—226
Permutation cube(s) reduced 224 225
Permutation(s), theory of 95 96
Perspective triangles 143—146
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